Modelagem de experimentos planejados com respostas discretas

Abstract

Many planned experiments present discrete values for the response variable. In these cases it is common practice to use Generalized Linear Models (GLM) to analyze the data. When m observations are taken (m>1) from each experimental unit (EU) the model should consider the variations between EU. However, it is known that that is not the case with GLM, casing diagnostics with overdispersion and lack of model adjustment. In this dissertation we present a justification for the use of Generalized Linear Mixed Model (GLMM) as an option for these cases, adding a random effect component to the linear predictor in order to capture the variation between EU. This is done comparing both analyses in simulated experiments with discrete responses (derived from either Binomial or Poisson distributions). We considered an EU experimental arrangement in a completely randomized design and simulated experiments in which we supposed that the effects of the EU were known. The responses from the treatments were to those of the EU in a linear model. From this, discrete responses were simulated using the inverse of the canonical link functions for Binomial and Poisson distributions. The resulting experiments were analyzed using GLMM and GLM. Analyses were conducted using R 2.14 software with 4000 simulations per configuration, with different m values. Comparisons were based on: Type I error rates, Residual Deviance, Akaike´s Information Criterion, Bayesian (Schwarz) Information Criterion and accuracy of estimated effects (related to known parametric values). For the Binomial case, the GLMM analysis preserved the type I error rates which did not occur with the GLM, in which the rates systemically exceeded the nominal values. For the Poisson case, GLMM analysis was also considerably more rigorous than GLM analysis. The information criteria of the adjustment were always better in GLMM than in GLM, the same occurring with the accuracy. In all analyzed situations the GLMM was more well-adjusted to the experimental data and should be used to replace GLM.